There are many countries that have strict banking laws. As always do your own due diligence and research.
Here are a few that I have had experience with.
Panama Is an American people friendly country and they have over 90 international banks there. Their Gov does not like our Gov much and the only reasons they will allow investigation into bank accounts are for murder and drug convictions.
Nevis Island has probably the most strict banking laws in the world that I know of. They can not divulge any account information by law or there are very harsh penalties. The are a small island in the West Indies and offer a lot of investment opportunities as well.
Dominica Is another that offers strict banking laws and they are also in the West Indies.
As always do your own research and due diligence.
Blessings